Victory for the ACT Student Text 15e

356 • S CIENCE

Passage X Radiometric dating is the process of determining the age of rocks from the decay of a radioactive element (decay is the spontaneous disintegration of a nucleus into a slightly lighter nucleus with the emission of subatomic particles, electromagnetic radiations, or both). The original element is called the parent isotope , and the element left behind after decay is called the daughter product . Rubidium-87, with a half-life of 48.8 billion years, decays into strontium-87, a stable isotope: PARENT DAUGHTER Rb Sr " β + − Strontium has several other isotopes that are also stable and do not decay, including strontium-86. Therefore, the ratio of strontium-87 to strontium-86 (Sr-87/ Sr-86) in a rock increases over time as rubidium-87 decays into strontium-87. 37 87 38 87 1 0

When magma (molten rock) cools and forms a rock, all parts of the rock have the same initial Sr-87/Sr-86 ratio because the two isotopes are uniformly mixed during the ϐŽ—‹† ƒ‰ƒ •–ƒ‰‡Ǥ ‘™‡˜‡”ǡ –Š‡ †‹ˆˆ‡”‡– minerals that form in rock accommodate varying quantities of rubidium, so different minerals will have different initial ratios of rubidium to strontium. With the passage of time, rubidium atoms frozen in place in mineral inclusions decay into strontium, so any increase in the quantity of strontium in a rock is attributable to an equal decrease in the quantity of rubidium (see Figure 1). Since the decrease in rubidium-87 is matched exactly by an increase in strontium-87, any decrease in the Rb- 87/Sr-87 ratio over time due to decay is proportional to the amount of rubidium-87 in the mineral at the time it froze into rock. Therefore, a line drawn through the points of the Rb-87/Sr-87 ratios for the mineral inclusion samples at a given time, called an isochron , is linear. The greater the slope of an isochron (the steeper the rate of climb), the older the minerals and therefore the rock that contains them.

T

P

Present Composition

T

2

Rubidium-87 Decays to Strontium-87

T

1

Sr-87/Sr-86

M

M

M

M

M

1

2

3

4

5

T

0

Initial Compositions of Minerals in the Rock

Rb-87/Sr-86

Figure 1